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  "body": "\n## Summary\n\nThe level-set method tracks a moving curve or surface as the zero [[level set|0B2RZ0778N]] of a function $\\phi(x, t)$ defined on a fixed grid.\nThe motion of the interface becomes a [[Hamilton–Jacobi equation|5TRXQKP7DY]] for $\\phi$, which is solved with finite difference schemes.\nIt was introduced by Stanley Osher and James Sethian.\nIts main strength is that merging and splitting of interfaces need no special treatment, and normals and curvature are computed from derivatives of $\\phi$.\nSee the [[definition|KT0380H39M]].\n\n## Explanations\n\n### L1 human\n\nThink of a landscape whose shoreline is the interface you want to follow.\nInstead of moving points along the shoreline, you raise or lower the whole landscape, and the shoreline moves by itself.\nIf two islands grow and touch, the shoreline simply changes its shape, with no bookkeeping.\nFor a circle of radius $r_0$ that grows at unit speed, the function $\\phi(x, t) = \\abs{x} - (r_0 + t)$ works: its zero set at time $t$ is the circle of radius $r_0 + t$.\n",
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